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<li><a class="reference internal" href="#">Probability calibration of classifiers</a></li>
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  <div class="sphx-glr-download-link-note admonition note">
<p class="admonition-title">Note</p>
<p>Click <a class="reference internal" href="#sphx-glr-download-auto-examples-calibration-plot-calibration-py"><span class="std std-ref">here</span></a> to download the full example code or to run this example in your browser via Binder</p>
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<div class="sphx-glr-example-title section" id="probability-calibration-of-classifiers">
<span id="sphx-glr-auto-examples-calibration-plot-calibration-py"></span><h1>Probability calibration of classifiers<a class="headerlink" href="#probability-calibration-of-classifiers" title="Permalink to this headline">¶</a></h1>
<p>When performing classification you often want to predict not only
the class label, but also the associated probability. This probability
gives you some kind of confidence on the prediction. However, not all
classifiers provide well-calibrated probabilities, some being over-confident
while others being under-confident. Thus, a separate calibration of predicted
probabilities is often desirable as a postprocessing. This example illustrates
two different methods for this calibration and evaluates the quality of the
returned probabilities using Brier’s score
(see <a class="reference external" href="https://en.wikipedia.org/wiki/Brier_score">https://en.wikipedia.org/wiki/Brier_score</a>).</p>
<p>Compared are the estimated probability using a Gaussian naive Bayes classifier
without calibration, with a sigmoid calibration, and with a non-parametric
isotonic calibration. One can observe that only the non-parametric model is
able to provide a probability calibration that returns probabilities close
to the expected 0.5 for most of the samples belonging to the middle
cluster with heterogeneous labels. This results in a significantly improved
Brier score.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="vm">__doc__</span><span class="p">)</span>

<span class="c1"># Author: Mathieu Blondel &lt;mathieu@mblondel.org&gt;</span>
<span class="c1">#         Alexandre Gramfort &lt;alexandre.gramfort@telecom-paristech.fr&gt;</span>
<span class="c1">#         Balazs Kegl &lt;balazs.kegl@gmail.com&gt;</span>
<span class="c1">#         Jan Hendrik Metzen &lt;jhm@informatik.uni-bremen.de&gt;</span>
<span class="c1"># License: BSD Style.</span>

<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">cm</span>

<span class="kn">from</span> <span class="nn">sklearn.datasets</span> <span class="kn">import</span> <span class="n">make_blobs</span>
<span class="kn">from</span> <span class="nn">sklearn.naive_bayes</span> <span class="kn">import</span> <span class="n">GaussianNB</span>
<span class="kn">from</span> <span class="nn">sklearn.metrics</span> <span class="kn">import</span> <span class="n">brier_score_loss</span>
<span class="kn">from</span> <span class="nn">sklearn.calibration</span> <span class="kn">import</span> <span class="n">CalibratedClassifierCV</span>
<span class="kn">from</span> <span class="nn">sklearn.model_selection</span> <span class="kn">import</span> <span class="n">train_test_split</span>


<span class="n">n_samples</span> <span class="o">=</span> <span class="mi">50000</span>
<span class="n">n_bins</span> <span class="o">=</span> <span class="mi">3</span>  <span class="c1"># use 3 bins for calibration_curve as we have 3 clusters here</span>

<span class="c1"># Generate 3 blobs with 2 classes where the second blob contains</span>
<span class="c1"># half positive samples and half negative samples. Probability in this</span>
<span class="c1"># blob is therefore 0.5.</span>
<span class="n">centers</span> <span class="o">=</span> <span class="p">[(</span><span class="o">-</span><span class="mi">5</span><span class="p">,</span> <span class="o">-</span><span class="mi">5</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">5</span><span class="p">,</span> <span class="mi">5</span><span class="p">)]</span>
<span class="n">X</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">make_blobs</span><span class="p">(</span><span class="n">n_samples</span><span class="o">=</span><span class="n">n_samples</span><span class="p">,</span> <span class="n">centers</span><span class="o">=</span><span class="n">centers</span><span class="p">,</span> <span class="n">shuffle</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span>
                  <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>

<span class="n">y</span><span class="p">[:</span><span class="n">n_samples</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
<span class="n">y</span><span class="p">[</span><span class="n">n_samples</span> <span class="o">//</span> <span class="mi">2</span><span class="p">:]</span> <span class="o">=</span> <span class="mi">1</span>
<span class="n">sample_weight</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">RandomState</span><span class="p">(</span><span class="mi">42</span><span class="p">)</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>

<span class="c1"># split train, test for calibration</span>
<span class="n">X_train</span><span class="p">,</span> <span class="n">X_test</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">y_test</span><span class="p">,</span> <span class="n">sw_train</span><span class="p">,</span> <span class="n">sw_test</span> <span class="o">=</span> \
    <span class="n">train_test_split</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">sample_weight</span><span class="p">,</span> <span class="n">test_size</span><span class="o">=</span><span class="mf">0.9</span><span class="p">,</span> <span class="n">random_state</span><span class="o">=</span><span class="mi">42</span><span class="p">)</span>

<span class="c1"># Gaussian Naive-Bayes with no calibration</span>
<span class="n">clf</span> <span class="o">=</span> <span class="n">GaussianNB</span><span class="p">()</span>
<span class="n">clf</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">)</span>  <span class="c1"># GaussianNB itself does not support sample-weights</span>
<span class="n">prob_pos_clf</span> <span class="o">=</span> <span class="n">clf</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>

<span class="c1"># Gaussian Naive-Bayes with isotonic calibration</span>
<span class="n">clf_isotonic</span> <span class="o">=</span> <span class="n">CalibratedClassifierCV</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;isotonic&#39;</span><span class="p">)</span>
<span class="n">clf_isotonic</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">sw_train</span><span class="p">)</span>
<span class="n">prob_pos_isotonic</span> <span class="o">=</span> <span class="n">clf_isotonic</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>

<span class="c1"># Gaussian Naive-Bayes with sigmoid calibration</span>
<span class="n">clf_sigmoid</span> <span class="o">=</span> <span class="n">CalibratedClassifierCV</span><span class="p">(</span><span class="n">clf</span><span class="p">,</span> <span class="n">cv</span><span class="o">=</span><span class="mi">2</span><span class="p">,</span> <span class="n">method</span><span class="o">=</span><span class="s1">&#39;sigmoid&#39;</span><span class="p">)</span>
<span class="n">clf_sigmoid</span><span class="o">.</span><span class="n">fit</span><span class="p">(</span><span class="n">X_train</span><span class="p">,</span> <span class="n">y_train</span><span class="p">,</span> <span class="n">sw_train</span><span class="p">)</span>
<span class="n">prob_pos_sigmoid</span> <span class="o">=</span> <span class="n">clf_sigmoid</span><span class="o">.</span><span class="n">predict_proba</span><span class="p">(</span><span class="n">X_test</span><span class="p">)[:,</span> <span class="mi">1</span><span class="p">]</span>

<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;Brier scores: (the smaller the better)&quot;</span><span class="p">)</span>

<span class="n">clf_score</span> <span class="o">=</span> <span class="n">brier_score_loss</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">prob_pos_clf</span><span class="p">,</span> <span class="n">sw_test</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;No calibration: </span><span class="si">%1.3f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">clf_score</span><span class="p">)</span>

<span class="n">clf_isotonic_score</span> <span class="o">=</span> <span class="n">brier_score_loss</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">prob_pos_isotonic</span><span class="p">,</span> <span class="n">sw_test</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;With isotonic calibration: </span><span class="si">%1.3f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">clf_isotonic_score</span><span class="p">)</span>

<span class="n">clf_sigmoid_score</span> <span class="o">=</span> <span class="n">brier_score_loss</span><span class="p">(</span><span class="n">y_test</span><span class="p">,</span> <span class="n">prob_pos_sigmoid</span><span class="p">,</span> <span class="n">sw_test</span><span class="p">)</span>
<span class="nb">print</span><span class="p">(</span><span class="s2">&quot;With sigmoid calibration: </span><span class="si">%1.3f</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">clf_sigmoid_score</span><span class="p">)</span>

<span class="c1"># #############################################################################</span>
<span class="c1"># Plot the data and the predicted probabilities</span>
<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">y_unique</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">unique</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="n">colors</span> <span class="o">=</span> <span class="n">cm</span><span class="o">.</span><span class="n">rainbow</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">y_unique</span><span class="o">.</span><span class="n">size</span><span class="p">))</span>
<span class="k">for</span> <span class="n">this_y</span><span class="p">,</span> <span class="n">color</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">y_unique</span><span class="p">,</span> <span class="n">colors</span><span class="p">):</span>
    <span class="n">this_X</span> <span class="o">=</span> <span class="n">X_train</span><span class="p">[</span><span class="n">y_train</span> <span class="o">==</span> <span class="n">this_y</span><span class="p">]</span>
    <span class="n">this_sw</span> <span class="o">=</span> <span class="n">sw_train</span><span class="p">[</span><span class="n">y_train</span> <span class="o">==</span> <span class="n">this_y</span><span class="p">]</span>
    <span class="n">plt</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">this_X</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">this_X</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">s</span><span class="o">=</span><span class="n">this_sw</span> <span class="o">*</span> <span class="mi">50</span><span class="p">,</span>
                <span class="n">c</span><span class="o">=</span><span class="n">color</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:],</span>
                <span class="n">alpha</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">edgecolor</span><span class="o">=</span><span class="s1">&#39;k&#39;</span><span class="p">,</span>
                <span class="n">label</span><span class="o">=</span><span class="s2">&quot;Class </span><span class="si">%s</span><span class="s2">&quot;</span> <span class="o">%</span> <span class="n">this_y</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">&quot;best&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Data&quot;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">order</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">lexsort</span><span class="p">((</span><span class="n">prob_pos_clf</span><span class="p">,</span> <span class="p">))</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">prob_pos_clf</span><span class="p">[</span><span class="n">order</span><span class="p">],</span> <span class="s1">&#39;r&#39;</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">&#39;No calibration (</span><span class="si">%1.3f</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="n">clf_score</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">prob_pos_isotonic</span><span class="p">[</span><span class="n">order</span><span class="p">],</span> <span class="s1">&#39;g&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
         <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Isotonic calibration (</span><span class="si">%1.3f</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="n">clf_isotonic_score</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">prob_pos_sigmoid</span><span class="p">[</span><span class="n">order</span><span class="p">],</span> <span class="s1">&#39;b&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
         <span class="n">label</span><span class="o">=</span><span class="s1">&#39;Sigmoid calibration (</span><span class="si">%1.3f</span><span class="s1">)&#39;</span> <span class="o">%</span> <span class="n">clf_sigmoid_score</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">y_test</span><span class="o">.</span><span class="n">size</span><span class="p">,</span> <span class="mi">51</span><span class="p">)[</span><span class="mi">1</span><span class="p">::</span><span class="mi">2</span><span class="p">],</span>
         <span class="n">y_test</span><span class="p">[</span><span class="n">order</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">25</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span>
         <span class="s1">&#39;k&#39;</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">r</span><span class="s1">&#39;Empirical&#39;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">([</span><span class="o">-</span><span class="mf">0.05</span><span class="p">,</span> <span class="mf">1.05</span><span class="p">])</span>
<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">&quot;Instances sorted according to predicted probability &quot;</span>
           <span class="s2">&quot;(uncalibrated GNB)&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">&quot;P(y=1)&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s2">&quot;upper left&quot;</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">&quot;Gaussian naive Bayes probabilities&quot;</span><span class="p">)</span>

<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
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